cant answer the first question but as for the second. It depends honestly in gaiden definitely promote as early as possible as growths are terrible in that game and the promotion gains are the difference between the base stat for that class and your current total in that stat. So if the base speed for a class is 10 and you have 4 speed you will gain 6 speed but if you have 11 speed when you class change then you will not gain anything in that stat. However growths have been buffed so you might want to take advantage of extra levels. Considering how early you can premote though and the fact that you get more than one promotion on most characters (and more if you get the class dlc) you will likely want to promote as soon as possible to start using the superior class.

My worst luck was Raven missing a 90 something hit then getting killed by a 1% hit 10% crit! He was using a sword enemy had an axe... sheer willpower was the only reason I switched my game off and set it down rather than throwing the sp across the room.
Edit: I have had Finn dodge a 100% chance hit once though due to prayer activating might be remember wrong but I was super impressed by it at the time.

Which games does this happen with? I mean I know Catria and Cordelia but other than that I am not sure. The pegknights with crushes in the gba games could always support and marry said crush if the player so chose.

Considering Ephraim and Eirika are supposed to promote when they use their bracelets to reclaim the sacred stones of their home it is entirely possible that they already had mounts that belonged to them in the stables and just reclaimed them, You don't HAVE to promote them there but thats more the game being nice and not forcing you to rush to level them to 20 before the chapter they promote.

Honestly the only way I would be okay for a fire emblem remake to have an avatar character is if it were Mark in fe7 the character already exists so it would be interesting to actually see them in action for once.